12 Mid-Chapter Quiz

Do you know HOW?

Each polygon below circumscribes the circle. Find the perimeter of the polygon.

Algebra Find the value of x in ⊙ O . circle dot o .

Find the value of each variable. Lines that appear to be tangent are tangent, and the dot represents the center.

Find m A B ⌢ m , modified eh b with frown above

Write a two-column proof, paragraph proof, or flow proof.

15. Proof Given: ⊙ A circle dot eh  with B C ¯ ≅ D E ¯ , A F ¯ ⊥ D E ¯ , A G ¯ ⊥ D E ¯ b c bar , approximately equal to . d e bar , comma . eh f bar , up tack . d e bar , comma . eh g bar , up tack , d e bar
    Prove: ∠ A F G ≅ ∠ A G F angle , eh f g approximately equal to , angle eh g f

    

16. Proof Given: ⊙ O circle dot o  with A D ⌢ ≅ B C ⌢ modified eh d with frown above , approximately equal to , modified b c with frown above
    Prove: Δ A B D ≅ Δ B A C cap delta , eh b d approximately equal to . cap delta b eh c

    

Do you UNDERSTAND?

17. Reasoning In ⊙ C ,   m P Q ⌢ = 50 circle dot c comma m , modified p q with frown above . equals 50  and m Q R ⌢ = 20 . m , modified q r with frown above . equals 20 .

    Find two possible values for m P R ⌢ m , modified p r with frown above

18. Open-Ended Draw a triangle circumscribed about a circle. Then draw the radii to each tangent. How many convex quadrilaterals are in your figure?

19. Reasoning E F ¯ e f bar  is tangent to both ⊙ A circle dot eh  and ⊙ B circle dot b  at F. C D ¯ c d bar  is tangent to ⊙ A circle dot eh  at C and to ⊙ B circle dot b  at D. What can you conclude about C E ¯ , D E ¯ , c e bar , comma . d e bar , comma  and F E ¯ ? f e bar , question mark  Explain.

    
20. Writing Explain why the length of a segment tangent to a circle from a point outside the circle will always be less than the distance from the point to the center of the circle.

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